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skullpatrol Group Title

Does 0.999...=1?

  • 2 years ago
  • 2 years ago

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  1. zzr0ck3r Group Title
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    .9999........ is not a number

    • 2 years ago
  2. zzr0ck3r Group Title
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    have you taken calculus?

    • 2 years ago
  3. zzr0ck3r Group Title
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    http://www.math.com/school/subject2/lessons/S2U2L1DP.html

    • 2 years ago
  4. zzr0ck3r Group Title
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    scroll down to number 4, its actaully an easy proof.

    • 2 years ago
  5. zzr0ck3r Group Title
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    you will enjoy calculus:)

    • 2 years ago
  6. carson889 Group Title
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    Here is an algebraic proof of it: 10x = 9.999999... with x = 0.99999... 10x - x = 9.99999... - 0.999999... 9x = 9 Thus, x = 1

    • 2 years ago
  7. zzr0ck3r Group Title
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    This question was asked because I was trying to exaplin that inbetween any two numbers is another number, he then said what about .9999999.... and 1, i then tried to explain to him that .99999999.. was not a finite number, then we had this question posted:)

    • 2 years ago
  8. zzr0ck3r Group Title
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    there is no amount of 9's that you can write after .9 that will make it equal to 1, but the limit as the amount of 9's goes to infinity is said to equal 1

    • 2 years ago
  9. ByteMe Group Title
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    wait... doesn't 0.9999... = 9/10 + 9/100 + 9/1000 + .... an infinite bounded series?

    • 2 years ago
  10. mayankdevnani Group Title
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    The number "0.9999..." can be "expanded" as: 0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

    • 2 years ago
  11. mayankdevnani Group Title
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    • 2 years ago
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  12. mayankdevnani Group Title
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    • 2 years ago
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  13. zzr0ck3r Group Title
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    lol, read this. then you will see the point of the question http://openstudy.com/study#/updates/50ab1ceee4b06b5e49334d38

    • 2 years ago
  14. mayankdevnani Group Title
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    So the formula proves that 0.9999... = 1.

    • 2 years ago
  15. mayankdevnani Group Title
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    @skullpatrol ok

    • 2 years ago
  16. zzr0ck3r Group Title
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    but .99999...is not a number is the point of this topic

    • 2 years ago
  17. mayankdevnani Group Title
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    0.999999..... is a no. we have tp prove that it is equal to 1

    • 2 years ago
  18. mayankdevnani Group Title
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    *to

    • 2 years ago
  19. zzr0ck3r Group Title
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    its a number if you think about convergence, but you can never write 1 in the form .999999999999, read the last question and you will see the point im trying to make

    • 2 years ago
  20. zzr0ck3r Group Title
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    its not a finite number.... it can be looked at as a sequence....at infinity then its a number. I told him that between any two numbers is another number, he then said what about .99999999999..... and 1, this is what followed.

    • 2 years ago
  21. zzr0ck3r Group Title
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    Its an extended real number in the since that infinity is an extended real number....

    • 2 years ago
  22. mayankdevnani Group Title
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    "But", some say, "there will always be a difference between 0.9999... and 1." Well, sort of. Yes, at any given stop, at any given stage of the expansion, for any given finite number of 9s, there will be a difference between 0.999...9 and 1. That is, if you do the subtraction, 1 – 0.999...9 will not equal zero. But the point of the "dot, dot, dot" is that there is no end; 0.9999... is inifinte. There is no "last" digit. So the "there's always a difference" argument betrays a lack of understanding of the infinite. (That's not a "criticism", per se; infinity is a messy topic.)

    • 2 years ago
  23. zzr0ck3r Group Title
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    right and i dont think he has had calculus...

    • 2 years ago
  24. zzr0ck3r Group Title
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    this started with density of rational/irational and archimedes principle on the real line

    • 2 years ago
  25. zzr0ck3r Group Title
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    the point is, that there is an infinite amount of numbers between any two numbers a,b where a != b

    • 2 years ago
  26. mayankdevnani Group Title
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    hahhaha.. we are just fighting you and me are absolutely right...it's a skull problem..right??

    • 2 years ago
  27. mayankdevnani Group Title
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    right?? @zzr0ck3r

    • 2 years ago
  28. zzr0ck3r Group Title
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    This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)

    • 2 years ago
  29. zzr0ck3r Group Title
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    right:)

    • 2 years ago
  30. mayankdevnani Group Title
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    :)

    • 2 years ago
  31. waterineyes Group Title
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    0.9999 is approximately equal to 1 but it is not exactly equal.. \[0.999 \approx 1 \qquad \qquad (0.999 \ne 1)\]

    • 2 years ago
  32. mayankdevnani Group Title
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    got it @skullpatrol

    • 2 years ago
  33. mayankdevnani Group Title
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    this question...lol

    • 2 years ago
  34. mayankdevnani Group Title
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    http://www.math.hmc.edu/funfacts/ffiles/10012.5.shtml

    • 2 years ago
  35. Zarkon Group Title
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    can you provide a proof of this ... "This one might make him want to quit math The infinite amount of numbers between 0,1 is larger than the infinite amount of numbers between 0 and infinity.:)"

    • 2 years ago
  36. zzr0ck3r Group Title
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    no, my analysis teacher said it two days ago. she said the elemnts between 0 and 1 have more mappings than 0-infinity

    • 2 years ago
  37. Zarkon Group Title
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    your teacher is either wrong or you have misquoted her

    • 2 years ago
  38. Zarkon Group Title
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    the real numbers between 0 and 1 is the same size as the real numbers from 0 to infinity

    • 2 years ago
  39. ParthKohli Group Title
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    \[1 - 0.999\cdots = 0.000\cdots = 0\]

    • one year ago
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